Embryoes likely begin differentiating with the first division. In order for areas of the body to develop in the appropriate position on the body the cells need to know their position in the body. This would most likely be accomplished by cells initially having a mechanism to turn groups of genes on or off so that they develop for the appropriate portion of the body.

Some research indicates that embryonic cells cannot each develop into all different cells. For example, an experiment to develop heart cells had to rely on watching for some of the embryonic cells in a dish to develop into cells that acted like heart cells.

VERY good question :) I'm not sure if there is a definative answer to that. Schultz et. al. (1999) proposed that a transcriptionally repressive state develops during the 2-cell stage (that transforms highly differentiated oocytes into totipotent blastomeres), where an increased histone deacetylation represses transcription.

The whole transcription machinery needs to be started again, which is sensitive to signals from the cells it is surrounded with. For me it is speculation what exactly happens at these very early stages, probably it is competition where the cells are competing against chemokines excreted by the others, when one cell takes the overhand it starts producing negative regulatory proteins that inhibit the other cells to differentiate in the same way. This then sets off a cascade that triggers the other cells to undertake other developmental routes.

You can read up on developmental biology to understand exactly how cells communicate are able to create complex architectures.

In vertebrates, the cells do not begin differentiating until after the 8-cell stage. Up until this point, the embryo could split in half and form twins.

If no differentiation occurs, how do you explain conjoined twins? they develop as mirror images connected at different locations, typically the torso or head, and occasionally share organs. Something in the programming causes both to develop heads at the same end and feet at the same end, unless you know of cases in which one develops upside down compared to the other.